sun

The Sun, in its T-Tauri phase, may have been losing mass at a rate of 10−8M⊙/yr for up to ten million years, ending with a mass M⊙. As a main sequence star, it loses mass at a rate of about 2×10−14M⊙/yr for ten billion years. As a red giant, it may lose up to 28% of the remaining mass. Estimate, in terms of M, the mass at the start of the T-Tauri phase, the mass of the remaining star at the end of the red giant phase. Round to two significant figures.

Yayy!! Done

First I found Mass at the 

T-Tauri stage by 

$M_{T-Tauri}=((M_{lost 1}*T_{1})*M_{\odot})+M_{\odot}$

where 

$M_{lost 1} = 1*10^-8M_{\odot}/yr$

and

$T_{1}=1*10^{10}years$

and 

$M_{\odot} = 1.989*10^{30}kg$

Then I found the mass when sun is a main sequence by 

$M_{main.sequence} = ((M_{lost2}*T_{2})*M_{\odot})-M_{\odot}))$

where 

$M_{lost2} = 2*10^{-14}M_{\odot}/yr$

 and

 $T_2=1*10^{10}years$

Finally I find the mass when sun is red giant by 

$M_{red.giant} =(28/100*M_{main.sequence})-M_{main.sequence}$

then I finnally divide the 

$\frac{M_{red.giant}}{T-Tauri}$